Dimensional Formula of Torque
The dimensional formula of torque is given by,
M1 L2 T-2
- M = Mass
- L = Length
- T = Time
Torque (T) = Moment of Inertia × Angular Acceleration . . . . (1)
Since, Moment of Inertia (M.O.I) = Radius of Gyration2 × Mass
∴ The dimensional formula of Moment of Inertia = M1 L2 T0 . . . (2)
And, Angular Acceleration = Angular velocity × Time-1
∴ The dimensional formula of Angular Acceleration = M0 L0 T-2 . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Torque = Moment of Inertia × Angular Acceleration
Or, I = [M1 L2 T0] × [M0 L0 T-2] = [M L2 T-2].
Therefore, the torque is dimensionally represented as [M L2 T-2].